2025 GESS PRELIMS P2 Q3

The diagram shows the points \(A\), \(B\), \(C\) and \(D\) on level ground, where \(D\) is due north of \(B\). \(CD=9\text{ m}\), \(AB=14.5\text{ m}\), \(AD=6\text{ m}\), angle \(DBC=30^\circ\) and angle \(DCB=85^\circ\).

1. Calculate the length of \(BD\).[2]
2. Calculate the bearing of \(A\) from \(D\).[3]
3. \(CT\) is a vertical pole of height \(12\text{ m}\) standing at \(C\). \(X\) is a point along the path \(BD\) such that the angle of elevation of the top of the pole, \(T\), from \(X\) is the greatest. Find the angle of elevation of \(T\) from \(X\).[3]